Non-commutative first order differential calculus over finitely generated associative algebras

TL;DR

This paper reviews the construction of first order differential calculi on finitely generated associative algebras, providing explicit methods and discussing optimal algebras, with detailed computations aimed at physicists.

Contribution

It offers an explicit construction of bimodules of one forms and discusses optimal algebras, advancing the understanding of non-commutative differential calculus.

Findings

Explicit construction of bimodule of one forms

Discussion of optimal algebras for calculi

Detailed computations for physicists

Abstract

In this review article the construction of first order coordinate differential calculi on finitely generated and finitely related associative algebras are considered and explicit construction of the bimodule of one form over such algebras is presented. The concept of optimal algebras for such calculi are also discussed. Detailed computations presented will make this note particularly useful for physicists.